12 hours a day is a two watch system. You are trying to read it too literally again. Take another look at MSM, Vol. III, Part B, Chapter 5 Manning, B5-5 Watchkeeping, (b) Two Watch Systems, on Page B5-4. That's how 8104 is interpreted in practice by the USCG. And it's what the tug owners do.
I wish the USCG would require three watches, but they don't, and they can't, because of section 8104
That's why tugs under 200 GRT can, and routinely do, operate on voyages over 600 miles with only 4 or 5 men in the crew. Every voyage to Alaska is 600 miles one way, before you even get into a 1200 mile plus round trip voyage. Most boats are 5 man boats. Some companies only run with 4 men. A few companies with 6 men. The USCG comes aboard but never questions it.
The union companies like Foss, Crowley, Dunlap are 6 men, but that is based upon the union agreement. Those companies also have a few boats over 200 GRT.
Tugs OVER 200 GRT on a voyage over 600 miles do require three watches because another law also applies. As I recall, its the Officers Competency Act (of 1935?) which implements an international treaty, SOLAS?
Another law (can't remember which one) requires licensed engineers on tugs over 300 GRT, that's why there is only a handful of US tugs over 300 GRT.